I. Introduction

II. Study Design and Material

Notation:

\[ \begin{aligned} k:& \text{subject}, k = 1,...,180\\ j:& \text{sequence}, j=0,1,2\\ i:& \text{period}, i=1,2,3\\ h:& \text{week}, h=1,2,3,4\\ \pi:& \text{period effect}\\ \tau:& \text{treatment effect}\\ \alpha:& \text{grouped treatment effects}\\ \beta:& \text{demographic effects}\\ \lambda:& \text{sequence/carryover effect}\\ \gamma:& \text{week effect}\\ b:& \text{subject-specific intercepts}\\ \mu:& \text{fixed-effect intercept}\\ \varepsilon:& \text{residual error}\\ \end{aligned} \]

Primary Objectives: Adverse Event

Proportion of Adverse Events per period

Patient Distribution: 30 people in per treatment sequence Initial Observation: Most patients do not face adverse events over the course of 4 weeks in each of the consecutive periods.

add demographic data

demographic summary

Distributional Summary of Predictor variables in the Study
	period1			period2			period3
Characteristic	No N = 164	Yes N = 16	p-value	No N = 168	Yes N = 12	p-value	No N = 163	Yes N = 17	p-value
age	31 (25, 37)	42 (40, 44)	<0.001	32 (25, 38)	40 (37, 44)	<0.001	32 (25, 38)	38 (32, 42)	0.012
¹ Median (Q1, Q3)
² Wilcoxon rank sum test

GLMM

Model Selection

LRT Between Model w/ and w/o Interaction Between Tx and Period
term	npar	AIC	BIC	logLik	minus2logL	statistic	df	p.value
glmm2	12	278.67	330.17	-127.34	254.67	NA	NA	NA
glmm1	16	281.34	350.01	-124.67	249.34	5.33	4	0.25

LRT Between Model w/ and w/o Race, Gender and Carryover Effect
term	npar	AIC	BIC	logLik	minus2logL	statistic	df	p.value
glmm3	7	271.25	301.29	-128.62	257.25	NA	NA	NA
glmm2	12	278.67	330.17	-127.34	254.67	2.57	5	0.77

Model Result (with Carryover Effect)

Characteristic	OR	95% CI	p-value
(Intercept)	0.00	0.00, 0.00	<0.001
Treatment
Pill A	—	—
Gel B	1.20	0.55, 2.64	0.6
Gel C	0.84	0.37, 1.92	0.7
Period
period1	—	—
period2	0.71	0.31, 1.64	0.4
period3	1.13	0.52, 2.46	0.8
Treatment Sequence
ABC or BAC	—	—
CAB or ACB	0.61	0.23, 1.62	0.3
BCA or CBA	0.84	0.35, 2.02	0.7
age	1.19	1.11, 1.27	<0.001
gender
Female	—	—
Male	0.90	0.43, 1.89	0.8
race
black	—	—
others	1.55	0.61, 3.95	0.4
white	1.74	0.65, 4.68	0.3
Abbreviations: CI = Confidence Interval, OR = Odds Ratio

Final Model Result (without Carryover Effect)

Notation: \[ \begin{aligned} \widehat{logit}(P(AE_{ijk} = 1)) &= b_{k} + \mu +\tau_{i} +\pi_j + \beta{a_{k}},\\ &\quad i = 1, 2, 3,\ j = 1, 2, 3,\ k = (1, 2, \ldots, 180),\\ &\quad b_{k} \sim N(0, {{\sigma}^2}_b) \end{aligned} \]

Characteristic	OR	95% CI	p-value
(Intercept)	0.00	0.00, 0.00	<0.001
Treatment
Pill A	—	—
Gel B	1.18	0.54, 2.58	0.7
Gel C	0.85	0.37, 1.94	0.7
Period
period1	—	—
period2	0.72	0.31, 1.65	0.4
period3	1.11	0.51, 2.40	0.8
age	1.19	1.12, 1.27	<0.001
Abbreviations: CI = Confidence Interval, OR = Odds Ratio

AE Prediction

Model Diagnostics

Secondary Objectives

**Table 1. Baseline Characteristics**
Characteristic	Overall N = 180¹	ABC N = 30¹	ACB N = 30¹	BAC N = 30¹	BCA N = 30¹	CAB N = 30¹	CBA N = 30¹	p-value²
Age (years)	32 (8) [18, 45]	33 (8) [19, 44]	31 (7) [18, 42]	31 (7) [20, 44]	33 (8) [19, 45]	32 (7) [21, 44]	31 (7) [20, 44]	0.6
Race								0.9
Black	64 (36%)	12 (40%)	13 (43%)	12 (40%)	10 (33%)	8 (27%)	9 (30%)
White	52 (29%)	8 (27%)	9 (30%)	7 (23%)	7 (23%)	12 (40%)	9 (30%)
Other	64 (36%)	10 (33%)	8 (27%)	11 (37%)	13 (43%)	10 (33%)	12 (40%)
Female	81 (45%)	13 (43%)	11 (37%)	16 (53%)	14 (47%)	12 (40%)	15 (50%)	0.8
¹ Mean (SD) [Min, Max]; n (%)
² Kruskal-Wallis rank sum test; Pearson’s Chi-squared test

preliminary assessment and comparison of systemic and local Pharmacokinetics (PK) of Pill A, Gel B, and Gel C and the correlation of PK with adherence measures and the occurrence of adverse events

Blood PK

\[ Y_{ik} = \mu + b_{k} + \pi_i + \tau_{i} + \lambda_{i} + \alpha_{ik} + \beta_{ik} + \varepsilon_{ik}, \quad b_{k} \sim N(0, \sigma_b^2), \quad \varepsilon_{ik} \sim N(0, \sigma^2) \]

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: bloodVL_change ~ treatment + overall_adhere + overall_safety +  
##     period + (1 | ptid)
##    Data: merged
## 
## REML criterion at convergence: 4827.4
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.5936 -0.5795  0.0153  0.6127  3.0873 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ptid     (Intercept)  23.09    4.805  
##  Residual             445.60   21.109  
## Number of obs: 540, groups:  ptid, 180
## 
## Fixed effects:
##                                Estimate Std. Error       df t value
## (Intercept)                     73.4552     6.7058 419.7422  10.954
## treatmentGel B                  -6.7916     2.3555 417.1354  -2.883
## treatmentGel C                  -9.0880     2.2967 391.5595  -3.957
## overall_adhere                   0.9365     0.1882 269.4894   4.975
## overall_safetyNo Adverse Event  26.4624     3.4675 521.9424   7.632
## periodperiod2                   -2.3295     2.2271 356.0129  -1.046
## periodperiod3                   -1.5433     2.2252 355.4545  -0.694
##                                            Pr(>|t|)    
## (Intercept)                    < 0.0000000000000002 ***
## treatmentGel B                              0.00414 ** 
## treatmentGel C                    0.000090106833765 ***
## overall_adhere                    0.000001161748202 ***
## overall_safetyNo Adverse Event    0.000000000000111 ***
## periodperiod2                               0.29629    
## periodperiod3                               0.48842    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) trtmGB trtmGC ovrll_ ov_NAE prdpr2
## treatmntGlB -0.437                                   
## treatmntGlC -0.359  0.538                            
## overall_dhr -0.832  0.328  0.247                     
## ovrll_sfNAE -0.616  0.080  0.032  0.196              
## periodperd2 -0.129 -0.009 -0.006 -0.026 -0.038       
## periodperd3 -0.173  0.001  0.001  0.004  0.009  0.499

Comparison	Beta	95% CI	p-value
Intercept (Pill A, Period 1, Sequence 0, No Adherence or AE)	73.5	60.3, 86.6	<0.001
Treatment
Gel B vs Pill A	-6.8	-11.4, -2.2	0.004
Gel C vs Pill A	-9.1	-13.6, -4.6	<0.001
Additional Day of Adherence	0.9	0.6, 1.3	<0.001
Adverse Event
No Adverse Event	26.5	19.7, 33.3	<0.001
Period
Period 2 vs Period 1	-2.3	-6.7, 2.1	0.3
Period 3 vs Period 1	-1.5	-5.9, 2.8	0.5
Abbreviation: CI = Confidence Interval

##  contrast       estimate   SE  df t.ratio p.value
##  Pill A - Gel B     6.79 2.36 417   2.882  0.0115
##  Pill A - Gel C     9.09 2.30 391   3.956  0.0003
##  Gel B - Gel C      2.30 2.24 359   1.027  0.5602
## 
## Results are averaged over the levels of: overall_safety, period 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: tukey method for comparing a family of 3 estimates

##  contrast          estimate   SE  df t.ratio p.value
##  period1 - period2    2.330 2.23 355   1.046  0.5484
##  period1 - period3    1.543 2.23 355   0.694  0.7674
##  period2 - period3   -0.786 2.23 356  -0.353  0.9337
## 
## Results are averaged over the levels of: treatment, overall_safety 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: tukey method for comparing a family of 3 estimates

Skin PK

Linear Model

## 
## Call:
## lm(formula = skinVL_change ~ treatment + overall_adhere + overall_safety + 
##     period, data = merged)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -112.388  -22.128    1.035   20.921  115.662 
## 
## Coefficients:
##                                Estimate Std. Error t value             Pr(>|t|)
## (Intercept)                    105.6003     9.9680  10.594 < 0.0000000000000002
## treatmentGel B                 -24.4131     3.6314  -6.723       0.000000000046
## treatmentGel C                 -36.9951     3.5493 -10.423 < 0.0000000000000002
## overall_adhere                   1.8154     0.2753   6.594       0.000000000103
## overall_safetyNo Adverse Event  55.7940     5.2166  10.696 < 0.0000000000000002
## periodperiod2                    0.8567     3.4535   0.248                0.804
## periodperiod3                    1.6225     3.4507   0.470                0.638
##                                   
## (Intercept)                    ***
## treatmentGel B                 ***
## treatmentGel C                 ***
## overall_adhere                 ***
## overall_safetyNo Adverse Event ***
## periodperiod2                     
## periodperiod3                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 32.74 on 533 degrees of freedom
## Multiple R-squared:  0.3581, Adjusted R-squared:  0.3508 
## F-statistic: 49.55 on 6 and 533 DF,  p-value: < 0.00000000000000022

Comparison	Beta	95% CI	p-value
Intercept (Pill A, Period 1, Sequence 0, No Adherence or AE)	105.6	86.0, 125.2	<0.001
Treatment
Gel B vs Pill A	-24.4	-31.5, -17.3	<0.001
Gel C vs Pill A	-37.0	-44.0, -30.0	<0.001
Additional Day of Adherence	1.8	1.3, 2.4	<0.001
Adverse Event
No Adverse Event	55.8	45.5, 66.0	<0.001
Period
Period 2 vs Period 1	0.9	-5.9, 7.6	0.8
Period 3 vs Period 1	1.6	-5.2, 8.4	0.6
Abbreviation: CI = Confidence Interval

##  contrast       estimate   SE  df t.ratio p.value
##  Pill A - Gel B     24.4 3.63 533   6.723 <0.0001
##  Pill A - Gel C     37.0 3.55 533  10.423 <0.0001
##  Gel B - Gel C      12.6 3.47 533   3.631  0.0009
## 
## Results are averaged over the levels of: overall_safety, period 
## P value adjustment: tukey method for comparing a family of 3 estimates

##  contrast          estimate   SE  df t.ratio p.value
##  period1 - period2   -0.857 3.45 533  -0.248  0.9666
##  period1 - period3   -1.623 3.45 533  -0.470  0.8853
##  period2 - period3   -0.766 3.45 533  -0.222  0.9733
## 
## Results are averaged over the levels of: treatment, overall_safety 
## P value adjustment: tukey method for comparing a family of 3 estimates

Linear Mixed Model

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: skinVL_change ~ treatment + overall_adhere + overall_safety +  
##     period + (1 | ptid)
##    Data: merged
## 
## REML criterion at convergence: 5269.4
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.4333 -0.6760  0.0316  0.6391  3.5333 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ptid     (Intercept)    0      0.00   
##  Residual             1072     32.74   
## Number of obs: 540, groups:  ptid, 180
## 
## Fixed effects:
##                                Estimate Std. Error       df t value
## (Intercept)                    105.6003     9.9680 533.0000  10.594
## treatmentGel B                 -24.4131     3.6314 533.0000  -6.723
## treatmentGel C                 -36.9951     3.5493 533.0000 -10.423
## overall_adhere                   1.8154     0.2753 533.0000   6.594
## overall_safetyNo Adverse Event  55.7940     5.2166 533.0000  10.696
## periodperiod2                    0.8567     3.4535 533.0000   0.248
## periodperiod3                    1.6225     3.4507 533.0000   0.470
##                                            Pr(>|t|)    
## (Intercept)                    < 0.0000000000000002 ***
## treatmentGel B                       0.000000000046 ***
## treatmentGel C                 < 0.0000000000000002 ***
## overall_adhere                       0.000000000103 ***
## overall_safetyNo Adverse Event < 0.0000000000000002 ***
## periodperiod2                                 0.804    
## periodperiod3                                 0.638    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) trtmGB trtmGC ovrll_ ov_NAE prdpr2
## treatmntGlB -0.429                                   
## treatmntGlC -0.354  0.534                            
## overall_dhr -0.826  0.311  0.234                     
## ovrll_sfNAE -0.627  0.079  0.033  0.206              
## periodperd2 -0.137 -0.008 -0.005 -0.025 -0.037       
## periodperd3 -0.180  0.001  0.001  0.004  0.009  0.499
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')

Comparison	Beta	95% CI	p-value
Intercept (Pill A, Period 1, Sequence 0, No Adherence or AE)	105.6	86.0, 125.2	<0.001
Treatment
Gel B vs Pill A	-24.4	-31.5, -17.3	<0.001
Gel C vs Pill A	-37.0	-44.0, -30.0	<0.001
Additional Day of Adherence	1.8	1.3, 2.4	<0.001
Adverse Event
No Adverse Event	55.8	45.5, 66.0	<0.001
Period
Period 2 vs Period 1	0.9	-5.9, 7.6	0.8
Period 3 vs Period 1	1.6	-5.2, 8.4	0.6
Abbreviation: CI = Confidence Interval

##  contrast       estimate   SE  df t.ratio p.value
##  Pill A - Gel B     24.4 3.63 412   6.721 <0.0001
##  Pill A - Gel C     37.0 3.55 388  10.422 <0.0001
##  Gel B - Gel C      12.6 3.47 359   3.631  0.0009
## 
## Results are averaged over the levels of: overall_safety, period 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: tukey method for comparing a family of 3 estimates

##  contrast          estimate   SE  df t.ratio p.value
##  period1 - period2   -0.857 3.45 356  -0.248  0.9666
##  period1 - period3   -1.623 3.45 355  -0.470  0.8853
##  period2 - period3   -0.766 3.45 356  -0.222  0.9733
## 
## Results are averaged over the levels of: treatment, overall_safety 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: tukey method for comparing a family of 3 estimates

Combined Table

Comparison	Blood Viral Load			Skin Viral Load
Comparison	Beta	95% CI	p-value	Beta	95% CI	p-value
Intercept (Pill A, Period 1, Sequence 0, No Adherence or AE)	73.5	60.3, 86.6	<0.001	105.6	86.0, 125.2	<0.001
Treatment
Gel B vs Pill A	-6.8	-11.4, -2.2	0.004	-24.4	-31.5, -17.3	<0.001
Gel C vs Pill A	-9.1	-13.6, -4.6	<0.001	-37.0	-44.0, -30.0	<0.001
Additional Day of Adherence	0.9	0.6, 1.3	<0.001	1.8	1.3, 2.4	<0.001
Adverse Event
No Adverse Event	26.5	19.7, 33.3	<0.001	55.8	45.5, 66.0	<0.001
Period
Period 2 vs Period 1	-2.3	-6.7, 2.1	0.3	0.9	-5.9, 7.6	0.8
Period 3 vs Period 1	-1.5	-5.9, 2.8	0.5	1.6	-5.2, 8.4	0.6
Abbreviation: CI = Confidence Interval

P9185 Project 1: Protocol of a Phase II MATIK Trial

Kate Colvin (kac2301), Chhiring Lama, Emily Carter